The inventive concepts described herein relate to a technology for reconstructing an image, and more particularly, relate to a method that reconstructs a high quality image by removing a noise in the image.
X-ray computed tomography (CT) refers to a technique for obtaining a high-quality image about the inner part of a human body by outputting a X-ray to the human body and detecting the X-ray passing through the human body. The X-ray CT is classified into a method of obtaining a 2-dimensional reconstruction image through a photography system including a radiation emission unit and a 1-dimensional detection unit and a method of obtaining a 3-dimensional reconstruction image through a photography system including a radiation emission unit and a 2-dimensional detection unit. Both of the two methods are used according to purposes and situations of a medical examination. Also, a method in which a trajectory of a radiation emission unit is helical has been developed to diagnose the whole human body.
However, the probability that a human body is exposed to a X-ray increases when X-ray is used, thereby causing cancers. Accordingly, low dose CT for reducing radiation dose in CT and minimizing exposed dose has been developed. An image signal obtained by the low dose CT includes a noise based on Poisson distribution. Because an image reconstructed in a conventional reconstruction method includes a noise, it is difficult to examine an internal state of a human body. An iterative reconstruction method is used to obtain a high-quality reconstruction image in which a noise is removed. A model based iterative reconstruction (MBIR) method is a representative iterative reconstruction method. The MBIR method iteratively reconstructs the high-quality reconstruction image by modeling the CT system.
The low dose X-ray CT may be modeled according to Equation 1.y=Aμ+ω.  [Equation 1]
In the equation 1, “y” means projection data measured from a detection unit. “A” means a projector generating projection data. “μ” is an image to be reconstructed. “ω” means a noise based on Poisson distribution. The following optimization problem may be solved to obtain a reconstruction image “μ” in which a noise is removed.
                                                        min              μ                        ⁢                                                                                                y                    -                    A                                    ⁣                  μ                                                            2                                +                      λ            ⁢                                                  ⁢                          R              ⁡                              (                μ                )                                      ⁢            ↵                          ⁢                                                      [                  Equation          ⁢                                          ⁢          2                ]            
“λ” means an adjustment parameter, and “R(μ)” means a regularization term. To solve the optimization problem, a projector A and a backprojector AT that performs a backprojection process with respect to projection data are repeated in order. The conventional iterative reconstruction method will be described with reference to FIG. 3. However, the above-described manner causes an increase in computation, and thus, it takes a long time to reconstruct an image.